The measurements of surface impedance for small regions are typically done by two approaches. The first approach is to create a small aperture on a screen to pass through the electromagnetic signal and the second approach is to use a system of lenses to focus the signal.
The first approach involves creating a small aperture on a metal screen through which the microwave field is coupled from a source on one side to a receiver on the other side. As such, when a material is placed over this aperture, the change in the transmitted field is related to the properties of the material. The problem with this approach is that the field at the aperture is not a plane wave and thus the response of the material to a plane wave is not being measured.
The second approach involves using a system of lenses to focus the signal traveling between a plane wave source and a plane wave. Such a focusing system can in principle concentrate the electromagnetic energy into a region approximately λ/3 in diameter, where λ is a wavelength of the electromagnetic wave. The problem with this approach is that by definition the size of the spot generated is a strong function of frequency so that if a region 3″ by 3″ is being examined at 2 GHz, the region shrinks to 0.3″ by 0.3″ at 20 GHz, thus any manufacturing inhomogeneities in the material become significant sources of noise at high frequency.
Another problem associated with the lens approach is the speed of light in the focal spot of a focused beam system is not equal to the speed of light in free space but is actually faster. Furthermore, it is also well known that the near radiating field in the neighborhood of the focal spot is full of “hotspots” where the amplitude and phase of the electromagnetic beam varies rapidly.
Since the simplest, most reliable, and most broadband method for extracting constitutive properties from an electromagnetic material measurement occurs under plane wave conditions, the ability to mimic a plane wave condition at the material sample is of paramount importance.